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It is not a common word. It was probably made up by the person who designed that quiz, or is a technical term that is used only under a particular school of specialists. '協調性' would be a more common word perhaps with a similar meaning.
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user458Aug 9 '11 at 14:00

All the answers indicate that this is a positive trait. Are we sure this isn't a negative trait like 付和雷同...? Like "I intend to cooperate because I can't take the lead by myself" or something?
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istrasciAug 9 '11 at 14:35

@istraci whether a trait is positive or negative depends on perception. E.g. "strong determination" may also be interpreted as "stubbornness" by some.
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FlawAug 10 '11 at 1:58

@sawa: This word is not seen by users, it is used internally by the quizz's designers.
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Nicolas RaoulAug 10 '11 at 2:43

The 8th result explains that 共同志向 is a term from a social psychology model, namely T. M. Newcomb's A-B-X system.

The definition above is given by an encyclopedia of communication theory that explains the A-B-X system.

Since the question context is about personality and the latter term is about an objective process in a relationship, I guess "communal orientation" is the source word for 共同志向性. So, the quiz can be asking how much you're willing to give without expecting anything in exchange.

Some of the other Google results show usages outside the context of academic psychology, like corporate mottos, but they're very few.